Developable mechanisms are a special class of mechanisms that can be placed on developable surfaces.<ref name=":0">{{Cite web|url=https://www.compliantmechanisms.byu.edu/about-developable-mechanisms|title=Developable Mechanisms {{!}} About Developable Mechanisms|website=compliantmechanisms|language=en|access-date=2019-02-13}}</ref><ref name=":2">{{cite journal |doi=10.1126/scirobotics.aau5171 |title=Developable mechanisms on developable surfaces |journal=Science Robotics |volume=4 |issue=27 |article-number=eaau5171 |year=2019 |last1=Nelson |first1=Todd G. |last2=Zimmerman |first2=Trent K. |last3=Magleby |first3=Spencer P. |last4=Lang |first4=Robert J. |last5=Howell |first5=Larry L. |pmid=33137737 |url=https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=3977&context=facpub |doi-access=free |url-access=subscription }}</ref>

== Examples == alt=Apollo Command Module door|thumb|371x371px|The door on the Apollo Command Module is an example of a simple developable mechanism because it conforms to the conical exterior of the Module, it moves, and its hinge line is aligned with the ruling lines of the conical surface. Some well-known examples of developable mechanisms include the door on the Apollo Command Module and the cargo doors on the Space Shuttle. Both of these examples are single-hinge-line mechanisms. Note how in each case the joint axes are in line with the ruling lines of the surface. Images are shown on the right.

Origami uses developable surfaces because the paper can be assumed to not stretch.<ref name="fromflatsheets">{{cite journal |doi=10.1016/j.mattod.2017.10.004 |title=From flat sheets to curved geometries: Origami and kirigami approaches |journal=Materials Today |volume=21 |issue=3 |pages=241–264 |year=2018 |last1=Callens |first1=Sebastien J.P. |last2=Zadpoor |first2=Amir A. |doi-access=free }}</ref> Action origami utilizes the movement of the origami.<ref>{{Cite thesis |last=Bowen|first=Landen|date=2013-07-02|title=A Study of Action Origami as Systems of Spherical Mechanisms |type=MS thesis |publisher=Brigham Young University |url=https://scholarsarchive.byu.edu/etd/3685 |hdl=1877/etd6391}}</ref><ref name="fromflatsheets" />

Ortho-planar mechanisms are a subset of developable mechanisms where the developable surface is a plane and the links emerge out of the plane.<ref>{{Cite thesis |last=Parise |first=John J. |date=1999 |title=Ortho-planar mechanisms |type=MS thesis |publisher=Brigham Young University |url=https://www.researchgate.net/publication/34191699 |language=en|access-date=2019-02-13}}</ref> Lamina Emergent Mechanisms are ortho-planar mechanisms (and hence also developable mechanisms) where the joints are compliant mechanisms.<ref>{{Cite thesis |last=Jacobsen|first=Joseph|date=2008-02-22|title=Fundamental Components for Lamina Emergent Mechanisms |type=MS thesis |publisher=Brigham Young University |url=https://scholarsarchive.byu.edu/etd/1330 |hdl=1877/etd2277}}</ref> The same joints used to create lamina emergent mechanisms can be used to approximate developable surfaces<ref name=":1">{{Cite thesis|last=Nelson|first=Todd|date=2018-06-01|title=Art to Engineering: Curved Folding and Developable Surfaces in Mechanism and Deployable Structure Design |type=PhD dissertation |publisher=Brigham Young University |url=https://scholarsarchive.byu.edu/etd/6865 |hdl=1877/etd10068}}</ref><ref>{{cite journal |doi=10.1115/1.4031901 |title=Facilitating Deployable Mechanisms and Structures Via Developable Lamina Emergent Arrays |journal=Journal of Mechanisms and Robotics |volume=8 |issue=3 |page=031006 |year=2016 |last1=Nelson |first1=Todd G. |last2=Lang |first2=Robert J. |last3=Pehrson |first3=Nathan A. |last4=Magleby |first4=Spencer P. |last5=Howell |first5=Larry L. }}</ref> alt=Space shuttle cargo doors|thumb|371x371px|The cargo doors on the space shuttle are simple developable mechanisms because they conform to the exterior of the shuttle during liftoff, they can move, and their hinge lines are aligned with the ruling lines of the shuttle.

== Advantages == Developable surfaces are easy to manufacture<ref>{{cite journal |last1=Chalfant |first1=Julie S. |last2=Maekawa |first2=Takashi |title=Design for Manufacturing Using B-Spline Developable Surfaces |journal=Journal of Ship Research |date=September 1998 |volume=42 |issue=3 |pages=207–215 |doi=10.5957/jsr.1998.42.3.207}}</ref> and are found in many applications. Developable mechanism can be embedded within these surfaces.<ref name=":2" />

Developable mechanisms are deployable.<ref name=":1" />

Developable mechanism stow compactly during one position of the mechanism's motion.<ref name=":0" /> <br />

== Mathematical Modeling == The motion of developable mechanisms can be modeled using traditional kinematics formulas. In rigid-body linkages, the shape of the rigid links does not change the motion.<ref>{{Cite book|title=Design of Machinery.|last=L.|first=Norton, Robert|date=2007|publisher=McGraw-Hill College|isbn=978-0-07-329098-0|oclc=150367304}}</ref>

== References == {{reflist}}

== External links == *[https://www.compliantmechanisms.byu.edu/about-developable-mechanisms About Developable Mechanisms] *[https://www.youtube.com/watch?v=CdPLzA4xIF0&t=6s Video about the applications and development of Developable Mechanisms]

Category:Mechanisms (engineering)